## UMEDA, Noriaki : COE Lecture Series

### On Global Existence and Blow-up of Solution of some Reaction-Diffusion Equations

My study has focused on non-negative solutions to the
initial value problem surrounding reaction-diffusion equations
and systems. Solutions to such equations formally represent various reaction-diffusion
phenomena, including temperature changes in substances that are caused by chemical reactions,
as well as changes in the numbers of individuals that exist in a mathematical ecology.
Ever since Hiroshi Fujita's seminal work in 1966, much
research has been done in this area. In particular, a number of researchers
are still actively studying the blow-up of solutions in finite time
and the existence of global solutions to reaction-diffusion equations.
In this talk, I am going to discuss a few aspects of this vast area of research,
with special attention to evaluation methods for blow-up and global solutions to such equations.